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Electric field drop exponentially

  1. Jan 28, 2008 #1
    Is there any situation where the electric field drop exponentially in free space? thanks
     
  2. jcsd
  3. Jan 29, 2008 #2

    mjsd

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    in free space? probably not...
    but across a surface where total internal reflection occurs, some evanescent wave is transmitted, this wave is exponentially suppressed.
     
  4. Jan 29, 2008 #3

    Andy Resnick

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    For electromagnetism, any near field amplitude component decays exponentially with distance.

    For electrostatics, I'm not sure. There may be a way to construct a set of charges such that the multipole expansion looks like the series expansion for an exponential function, but I have never seen one.
     
  5. Jan 30, 2008 #4

    Claude Bile

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    Evanescent (exponentially decaying fields) can be produced by;

    - Total internal reflection.
    - Guided modes in a waveguide.
    - An EM diffracting off a sub-wavelength aperture or obstacle (Near-field).
    - Exciting a charged surface at resonance (surface plasmons).

    Claude.
     
  6. Jan 30, 2008 #5
    > For electrostatics, I'm not sure. There may be a way to construct a set of charges such that the multipole expansion looks like the series expansion for an exponential function

    Or put a dielectric with spatially varying dielectric constant around a point charge in a homocentric manner. This would eliminate the inverse square and introduce the exponential. Here it is:

    E = 1/4πε(r) Q / r^2

    if ε(r) = a * exp(br) / r^2

    then you've got a decaying exponential effect.

    E = E0 * exp(-br)
     
    Last edited: Jan 30, 2008
  7. Jan 30, 2008 #6
    a field whose magnitude decays exponentially (either in 1-D or radially from some central point) has a non-zero divergence everywhere. so if by "free space" you mean no charge density, then I don't think such a field could exist anywhere in free space.
     
    Last edited: Jan 30, 2008
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